| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Matrices |
| Type | Matrix arithmetic operations |
| Difficulty | Easy -1.2 This is a straightforward Further Maths question testing basic matrix operations: scalar multiplication, subtraction, and finding the inverse of a 2×2 matrix using the standard formula. Both parts are direct applications of standard procedures with no problem-solving required. While it's FP1, these are foundational matrix skills that are purely procedural. |
| Spec | 4.03b Matrix operations: addition, multiplication, scalar4.03n Inverse 2x2 matrix |
| Answer | Marks | Guidance |
|---|---|---|
| Answer: \(\begin{pmatrix}2a-3 & 2\\2 & 5\end{pmatrix}\) | B1, B1, B1, B1 [3] | 1 or 3l seen or used; 2 elements correct; Other 2 elements correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer: \(\frac{1}{4a-1}\begin{pmatrix}4 & -1\\-1 & a\end{pmatrix}\) or equivalent | B1, B1 [2] | Divide by correct determinant; Both diagonals correct |
### (i)
Answer: $\begin{pmatrix}2a-3 & 2\\2 & 5\end{pmatrix}$ | B1, B1, B1, B1 [3] | 1 or 3l seen or used; 2 elements correct; Other 2 elements correct
### (ii)
Answer: $\frac{1}{4a-1}\begin{pmatrix}4 & -1\\-1 & a\end{pmatrix}$ or equivalent | B1, B1 [2] | Divide by correct determinant; Both diagonals correctThe matrix A is given by $A = \begin{pmatrix} a & 1 \\ 1 & a \end{pmatrix}$, where $a \neq \frac{1}{2}$, and I denotes the $2 \times 2$ identity matrix. Find
\begin{enumerate}[label=(\roman*)]
\item $2A - 3I$, [3]
\item $A^{-1}$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP1 2013 Q1 [5]}}